Piggy Tower replaces the old practice mode and warm-up rounds, and it is used to teach new players how the game works. Piggy Tower consists of floors that have 1-4 levels each. In order to unlock the next floor, you will need to collect a certain amount of green stars. You get stars based on your score in the levels (each passed level can give up to 3 stars).
The first 9 floors are each teaching one new bird, and on the 10th floor you unlock the Tournament feature. The floors after that are for mastering your skills. The current maximum floor is 36, which is why there is a cloud covering everything above that.
As this feature is intended for new players, it is not currently available on the oldest accounts.